Define an equivalence relation. Show that the relation similarity on the set of all triangles in a plene is an equivalence relation.

Show that the relation is congruent to on the set T of all triangles in a plane is an equivalence relation.

Show that the relation R in the set Z of intergers given by R ={(a,b):2 divides a-b } is an equivalence relation.

Which one of the following relations on R is an equivalence relation?

Show that the relation R on the set A={1,2,3,4,5} given by R={(a,b):|a-b| is even} is an equivalence relation.

The relation 'less than' in the set of natural numbers is

Show that the relation is a subset of on the set of all sets is reflexive and transitive but not symmetric on S.

In the set of integers Z, which of the following relation R is not an equivalence relation ?

Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; S={(m/n , p/q)"m , n , pandqa r ei n t e g e r ss u c ht h a tn ,q"!="0andq m = p n"} . Then (1) neither R nor S is an equivalence relation (2) S is an equivalence relation but R is not an equivalence relation (3) R and S both are equivalence relations (4) R is an equivalence relation but S is not an equivalence relation

On a given set AA define the smalest and the large equivalence relation.

Define specific and equivalent conductance. How are they related ?